BLIND AND COMPLETE MODELING OF LINEAR SYSTEMS USING THIRD ORDER CUMULANTS

This paper presents a novel approach to structure determination of linear systems along with the choice of system orders and parameters. AutoRegressive （AR）, Moving Average （MA） or AutoRegressive-Moving Average （ARMA） model structure can be extracted blindly from the Third Order Cumulants （TOC） of the system output ts, where the unknown system is driven by an unobservable stationary independent identically distributed （i.i.d.） non-Gaussian signal. By means of the system order recursion, whether the system has an AR structure or has AR part of an ARMA structure is firstly investigated. MA features in the TOC domain is then applied as a threshold to decide if the system is an MA model or has MA part of an ARMA model. Numerical simulations illustrate the generality of the proposed blind structure identification methodology that may serve as a guideline for blind, linear system modeling.

Signal Classification Method Based on Support Vector Machine and High-Order Cumulants

In this paper, a classification method based on Support Vector Machine (SVM) is given in the digital modulation signal classification. The second, fourth and sixth order cumulants of the received signals are used as classification vectors firstly, then the kernel thought is used to map the feature vector to the high dimensional feature space and the optimum separating hyperplane is constructed in space to realize signal recognition. In order to build an effective and robust SVM classifier, the radial basis kernel function is selected, one against one or one against rest of multi-class classifier is designed, and method of parameter selection using cross- validation grid is adopted. Through the experiments it can be concluded that the classifier based on SVM has high performance and is more robust.

Application of Three Order Cumulants in Fault Diagnosis

The three-order cumulants’ complex forms of different definitions include different coupling information of signals, and the information can be used to diagnose fault. In the experiment of pressure reducing valve’s fault diagnosis, through these different coupling information, the features of fault signals and normal signals were extracted by wavelet in different directions, then these features were inputted to diagnose the fault. The experiment shows that this method can achieve a satisfactory result.

Recognition Analysis and Simulation Implementation Based on High-Order Cumulants of Wireless Digital Modulation Mode

This paper mainly studies the data characteristics of high order cumulants using digitally modulated signals, and constructs the identification feature parameters that can distinguish the signal modulation type by the high-order cumulants data of the digital modulation signal. Set the identification signal modulation type determination threshold based on the value of the identification feature parameter. The identification feature parameter value of the signal modulation type is compared with the set determination threshold, to realize the recognition of digital modulation signal. This identification method is implemented based on MATLAB design, with a 2ASK (2-ary Amplitude Shift Keying) signal, 4ASK (4-ary Amplitude Shift Keying) signal, 2PSK (2-ary Phase Shift Keying) signal, 4PSK (4-ary Phase Shift Keying) signal, 2FSK (2-ary Frequency Shift Keying) signal, 4FSK (4-ary Frequency Shift Keying) signal. The second, fourth and sixth order cumulants of the six signals were analyzed. Calculate the selected identification feature parameter value and the determination threshold to identify the six signals. The six signals have made MATLAB identification simulation. Simulation results show that this method is feasible and has high recognition rate. Simulation results verify that such recognition methods maintain a high recognition rate under conditions with low signal-to-noise ratio. This identification method can be extended to more MASK (M-ary Amplitude Shift Keying), MPSK (M-ary Phase Shift Keying), MFSK (M-ary Frequency Shift Keying), MQAM (M-ary Quadrature Amplitude Modulation) signal identification.

Resolution performance analysis of cumulants-based rank reduction estimator in presence of unexpected modeling errors

Compared to the rank reduction estimator （RARE） based on second-order statistics （called SOS-RARE）, the RARE employing fourth-order cumulants （referred to as FOC-RARE） is capable of dealing with more sources and mitigating the negative influences of the Gaussian colored noise. However, in the presence of unexpected modeling errors, the resolution behavior of the FOC-RARE also deteriorate significantly as SOS-RARE, even for a known array covariance matrix. For this reason, the angle resolution capability of the FOC-RARE was theoretically analyzed. Firstly, the explicit formula for the mathematical expectation of the FOC-RARE spatial spectrum was derived through the second-order perturbation analysis method. Then, with the assumption that the unexpected modeling errors were drawn from complex circular Gaussian distribution, the theoretical formulas for the angle resolution probability of the FOC-RARE were presented. Numerical experiments validate our analytical results and demonstrate that the FOC-RARE has higher robustness to the unexpected modeling en＇ors than that of the SOS-RARE from the resolution point of view.

THE FOURTH-ORDER CUMULANTS BASED SPECTRALESTIMATION METHOD AND ITS APPLICATIONTO DIRECTION-FINDING

Traditional approaches of spatial spectral estimation are usually based on the second-order statistics. The higher-order cumulants and the poly-spectrum contain more information and are capable of reducing the Gaussian noise. In this paper, we present a new spectrum estimation method for direction-finding, the FOMUSIC algorithm, which is based on the eigen-structure analysis of the fourth-order cumulants. The derivation of the algorithm is given in detail and its performance is illustrated by both the computer simulations and the experiments of a direction-finding system. The obtained results demonstrate that the fourth-order cumulants based method outperforms the traditional methods, especially when the noise is an unknown colored one.

The Application of Coupled Three Order Cumulants’ Differential Feature in Fault Diagnosis

Complex three-order cumulant has different definition forms. Different forms conclude different information. For studying the effection of frequency in the coupled signals to fault diagnosis, the differential method to the three order cumulants of coupled signals is adopted. By using the differential of complex three order cumulants before and after respectively, then their ?dimensional spectrum is calculated, and the results are used to fault diagnosis. The experimental results show that, the increase frequency item in three order cumulants after differentiated impacts on the results of fault diagnosis and the degree of effection is relative to the differential times. And the correct rate of fault diagnosis can be raised by changing the differential times of three order cumulants.

Joint estimation of DOA, frequency, and polarization based on cumulants and UCA

A joint estimation algorithm of direction of arrival （DOA）, frequency, and polarization, based on fourth-order cumulants and uniform circular array （UCA） of trimmed vector sensors is presented for narrowband non-Gaussian signals. The proposed approach, which is suitable for applications in arbitrary Gaussian noise environments, gives a closed-form representation of the estimated parameters, without spectral peak searching. An efficient method is also provided for elimination of cyclic phase ambiguities. Simulations are presented to show the performance of the algorithm.

ROBUST MODULATION CLASSIFIER BASED ON CUMULANTS FOR MDPSK WITH FREQUENCY OFFSET

This paper presents an improved algorithm for classification of M-Differential Phase-Shift Keying(MDPSK) signals based on eumulant. The feature proposed in the algorithm is invariant with respect to constellation scale, rotation, the shift and the carrier frequency offset between transmitter and receiver.The invariant property is proved theoretically.Through computer simulation the performance is evaluated and the results show that the improved classification algorithm is better and valuable in practice.

Moments and Cumulants of Diffraction Profiles Broadened by Stacking Faults

Line broadening in a diffraction intensity profile of powdered crystalline materials due to stacking fault has been characterized in terms of the zeroth, first, second, third, and fourth moments and the fourth cumulant. Calculations have been derived showing that the first moment causes a shift in the peak position of the profile while the third moment affects its shape. The intensity expression has been derived on the basis of usual Cartesian coordinates and also of polar coordinates indicated by the probability of the fault and the reciprocal lattice parameter as the two axes. The expressions for the fourth cumulant have also been so derived. Here we have used three different approaches to determine methods for calculating the fourth cumulant due to stacking faults. The three forms of the equations derived here are for different coordinate systems, but will arrive at the same answers.

The Application of Cumulants Slices in Fault Diagnosis

Complex third-order cumulant has different definition forms. Different forms have different coupling properties, and the generated complex cumulants slices contain different coupling information of signals. In experiments, using the different definitions, the same coupling method is applied to both specific fault signals and normal signals. Furthermore, complex third-order cumulant slices spectrum is defined, and it is used to analyse the coupling features of normal signals and fault signals. Experiments indicate that the detection accuracy rate on the same fault is not the same with the different coupling method, thus, it provides an alternative method to diagnose the specific fault.

The Application of Three Order Cumulants Coupling Features in Fault Diagnosis

Although mechanical vibration is extremely complicated, each fault signal produced by it has its own inherent features, The distinction may be most prominent between the certain components hidden in those features and the same components of normal signals. Three-order cumulant can reduce the Gaussian background noise automatically and its complex formal includes different coupling information of its signal. In the experiment, through these different coupling modes, the same coupling components are fetched from specific fault signal and normal signal, then these components are used to diagnose that certain fault. The results show that the method can fetch the most prominent distinction between normal signal and the specific fault signal, so the specific fault diagnosis by this method is satisfactory.

Fixed point behavior of cumulants in the three-dimensional Ising universality class

High-order cumulants and factorial cumulants of conserved charges are suggested for the study of the critical dynamics in heavy-ion collision experiments. In this paper, using the parametric representation of the threedimensional Ising model which is believed to belong to the same universality class as quantum chromo-dynamics,the temperature dependence of the second-to fourth-order(factorial) cumulants of the order parameter is studied. It is found that the values of the normalized cumulants are independent of the external magnetic field at the critical temperature, which results in a fixed point in the temperature dependence of the normalized cumulants. In finite-size systems simulated using the Monte Carlo method, this fixed point behavior still exists at temperatures near the critical. This fixed point behavior has also appeared in the temperature dependence of normalized factorial cumulants from at least the fourth order. With a mapping from the Ising model to QCD, the fixed point behavior is also found in the energy dependence of the normalized cumulants(or fourth-order factorial cumulants) along different freezeout curves.

Cumulative effects of excess high-normal alanine aminotransferase levels in relation to new-onset metabolic dysfunction-associated fatty liver disease in China

BACKGROUND Within the normal range,elevated alanine aminotransferase(ALT)levels are associated with an increased risk of metabolic dysfunction-associated fatty liver disease(MAFLD).AIM To investigate the associations between repeated high-normal ALT measurements and the risk of new-onset MAFLD prospectively.METHODS A cohort of 3553 participants followed for four consecutive health examinations over 4 years was selected.The incidence rate,cumulative times,and equally and unequally weighted cumulative effects of excess high-normal ALT levels(ehALT)were measured.Cox proportional hazards regression was used to analyse the association between the cumulative effects of ehALT and the risk of new-onset MAFLD.RESULTS A total of 83.13%of participants with MAFLD had normal ALT levels.The incidence rate of MAFLD showed a linear increasing trend in the cumulative ehALT group.Compared with those in the low-normal ALT group,the multivariate adjusted hazard ratios of the equally and unequally weighted cumulative effects of ehALT were 1.651[95%confidence interval(CI):1.199-2.273]and 1.535(95%CI:1.119-2.106)in the third quartile and 1.616(95%CI:1.162-2.246)and 1.580(95%CI:1.155-2.162)in the fourth quartile,respectively.CONCLUSION Most participants with MAFLD had normal ALT levels.Long-term high-normal ALT levels were associated with a cumulative increased risk of new-onset MAFLD.

Mechanical responses of anchoring structure under triaxial cyclic loading

Dynamic load on anchoring structures(AS)within deep roadways can result in cumulative damage and failure.This study develops an experimental device designed to test AS under triaxial loads.The device enables the investigation of the mechanical response,failure mode,instability assessment criteria,and anchorage effect of AS subjected to combined cyclic dynamic-static triaxial stress paths.The results show that the peak bearing strength is positively correlated with the anchoring matrix strength,anchorage length,and edgewise compressive strength.The bearing capacity decreases significantly when the anchorage direction is severely inclined.The free face failure modes are typically transverse cracking,concave fracturing,V-shaped slipping and detachment,and spallation detachment.Besides,when the anchoring matrix strength and the anchorage length decrease while the edgewise compressive strength,loading rate,and anchorage inclination angle increase,the failure intensity rises.Instability is determined by a negative tangent modulus of the displacement-strength curve or the continued deformation increase against the general downward trend.Under cyclic loads,the driving force that breaks the rock mass along the normal vector and the rigidity of the AS are the two factors that determine roadway stability.Finally,a control measure for surrounding rock stability is proposed to reduce the internal driving force via a pressure relief method and improve the rigidity of the AS by full-length anchorage and grouting modification.

Spatiotemporal changes of gross primary productivity and its response to drought in the Mongolian Plateau under climate change

Gross primary productivity(GPP)of vegetation is an important constituent of the terrestrial carbon sinks and is significantly influenced by drought.Understanding the impact of droughts on different types of vegetation GPP provides insight into the spatiotemporal variation of terrestrial carbon sinks,aiding efforts to mitigate the detrimental effects of climate change.In this study,we utilized the precipitation and temperature data from the Climatic Research Unit,the standardized precipitation evapotranspiration index(SPEI),the standardized precipitation index(SPI),and the simulated vegetation GPP using the eddy covariance-light use efficiency(EC-LUE)model to analyze the spatiotemporal change of GPP and its response to different drought indices in the Mongolian Plateau during 1982-2018.The main findings indicated that vegetation GPP decreased in 50.53% of the plateau,mainly in its northern and northeastern parts,while it increased in the remaining 49.47%area.Specifically,meadow steppe(78.92%)and deciduous forest(79.46%)witnessed a significant decrease in vegetation GPP,while alpine steppe(75.08%),cropland(76.27%),and sandy vegetation(87.88%)recovered well.Warming aridification areas accounted for 71.39% of the affected areas,while 28.53% of the areas underwent severe aridification,mainly located in the south and central regions.Notably,the warming aridification areas of desert steppe(92.68%)and sandy vegetation(90.24%)were significant.Climate warming was found to amplify the sensitivity of coniferous forest,deciduous forest,meadow steppe,and alpine steppe GPP to drought.Additionally,the drought sensitivity of vegetation GPP in the Mongolian Plateau gradually decreased as altitude increased.The cumulative effect of drought on vegetation GPP persisted for 3.00-8.00 months.The findings of this study will improve the understanding of how drought influences vegetation in arid and semi-arid areas.

Hierarchical space–time block codes signals classification using higher order cumulants

An efficient method for blind classification of space time block codes （STBCs） based on fourth-order cumulants is proposed for a single receiver antenna. This paper presents a model of received STBCs signals in multiple input single output （MISO） communication systems and applies the characteristics of coding matrices to derive analytical expressions for the fourth-order cumu- lants to be used as the basis of an algorithm. The fourth-order cumulants at various delay vectors present non-null values that depend on the transmitted STBCs. Tests of nullity are accomplished by hypothesis testing. The proposed algorithm avoids the need for a priori information of modulation scheme, channel coefficients, and noise power. Consequently, it is well suited for non-cooperative scenarios. Simulations show that this method performs well even at low signal-to-noise ratios （SNRs）.

High cumulants of conserved charges and their statistical uncertainties

We study the influence of measured high cumulants of conserved charges on their associated statistical uncertainties in relativistic heavy-ion collisions. With a given number of events, the measured cumulants randomly fluctuate with an approximately normal distribution, while the estimated statistical uncertainties are found to be correlated with corresponding values of the obtained cumulants. Generally, with a given number of events, the larger the cumulants we measure, the larger the statistical uncertainties that are estimated. The error-weighted averaged cumulants are dependent on statistics. Despite this effect, however, it is found that the three sigma rule of thumb is still applicable when the statistics are above one million.

Second-order cumulants ghost imaging

Ghost imaging(GI)is a technique to retrieve images by correlating intensity fluctuations.In this Letter,we present a novel scheme for GI referred to as second-order cumulants GI(SCGI).The image is retrieved from fluctuation information,and resolution may be enhanced compared to traditional GI.We experimentally performed SCGI image reconstruction,and the results are in agreement with theoretical predictions.

A recursive calculating algorithm for higher-order cumulants over sliding window and its application in speech endpoint detection

Regarding the performance of traditional endpoint detection algorithms degrades as the environment noise level increases, a recursive calculating algorithm for higher-order cu- mulants over a sliding window is proposed. Then it is applied to the speech endpoint detection. Furthermore, endpoint detection is carried out with the feature of energy. Experimental results show that both the computational efficiency and the robustness against noise of the proposed algorithm are improved remarkably compared with traditional algorithm. The average prob- ability of correct point detection （Pc-point） of the proposed voice activity detection （VAD） is 6.07% higher than that of G.729b VAD in different noisy at different signal-noise ratios （SNRs） environments.